The longest wavelength in physics or mathematics is typically associated with the concept of infinite wavelength or zero frequency. However, it is important to note that "wavelength" refers to the distance between consecutive points in a wave that are in phase with each other. In physical terms, it is often used to describe electromagnetic waves, such as light.
For electromagnetic waves, the wavelength can range from extremely short, such as gamma rays with wavelengths on the order of picometers (10^-12 meters), to extremely long, such as radio waves with wavelengths on the order of kilometers. However, beyond radio waves, there is no strict upper limit on wavelength.
In the mathematical realm, the concept of wavelength is not as precisely defined. Wavelength is mainly used in the context of waves, and different mathematical functions can represent waves with different wavelengths. In theory, the wavelength of a mathematical wave can be arbitrarily long, but it is still finite in a mathematical sense.
To summarize, in the physical world, the longest wavelength is associated with radio waves, which can have wavelengths on the order of kilometers or longer. In the mathematical world, there is no strict upper limit on wavelength, but it remains finite within the context of the mathematical functions used to describe waves.